4.1. Force

We have seen that the principal function of muscle is to exert force. In 1687, Isaac Newton published his three-volume Philosophiæ Naturalis Principia Mathematica (Mathematical Principles of Natural Philosophy) on classical mechanics. It is often referred to simply as Principia or Principia Mathematica and contains his proposed three laws of motion. The concept of force comes from the first of these laws. The expression of this law in its original Latin text together with the translation (Cajori, 1960) is:

The SI unit of force is the newton (N). For linear motion, if force is applied to a stationary or moving object it tends to accelerate that object. The reluctance of the object to accelerate is attributable to its mass. The SI unit for mass is the kilogram (kg). From Newton's first law, the mass of an object represents its inertia – that is, the body's reluctance to change its state of motion. Because of the effect of gravity, this mass exerts a force and this force is the weight of the object. Weight and mass are still sometimes confused, especially in the contexts of body weight and cycle ergometry. Body weight should be reported in newtons, body mass in kilograms.

In many instances, we are interested not only in the linear effect of the forces that are acting but also on the angular effects they produce. The moment of a force (i.e. its torque) is the product of the force and its perpendicular distance from the axis about which either the body rotates or attempts to rotate. The reluctance of a body to change its state of angular motion is its moment of inertia and this property is related both to the body's mass and the distribution of this mass about the rotational axis. This is important in the context of exercise because the action of muscle is commonly experienced as a moment about the related joint and not as a linear force.

A principal interest of physiologists is mechanisms that explain muscle's ability to exert force and, in particular, those that explain or accompany fatigue in which muscle's ability to exert force is reduced.

4.2 Work

Mechanical work done is a concept from classical mechanics outlined in Newton's Principia and occurs when:

Displacement is a vector quantity in that it has both magnitude and direction, whereas distance is a scalar quantity that has magnitude but without specification of direction. With that note of caution, mechanical work done tends to be considered as the distance through which the point of application of a force moves. Consequently, it is calculated as the product of the force and the distance over which that force is applied. The SI unit of distance is the metre (m) so, as indicated in Table I, mechanical work done is represented as N · m and the SI unit is the joule (J). One joule of mechanical work is done when a force of 1 N moves through a distance of 1 m.

Consider, then, isometric muscle activity. A great force could be exerted by the biceps to oppose the weight of an object with the hand. Since the hand will not move if the weight is beyond the capability of the muscle to act through its associated lever system or if the degree of muscle activation is moderated to produce a moment equal in magnitude but opposite in direction to that produced by the weight, mechanical work done is zero.

During consideration of mechanical work done, boundaries of the related energetic or thermodynamic system have to be specified. The work done represents the change in net energy of the entire system. For example, during a movement the system might be defined as the entire body or, alternatively, as only a single limb or segment. Conventionally, for exercise a distinction is made between the concepts of internal and external work (Winter, 2004).

Internal work is the mechanical work done to change the mechanical energy of different parts of the system (e.g. to move one or more limbs), with no change in the energy of the total system. External work is that done which does bring about a change in the total energy of the system. However, this does not capture all of the mechanical work that might be done. For instance, during the initial stages of activation and force development, parallel and series elastic components in muscle stretch as the active muscle shortens. When all of the elastic components have been stretched to their limit, no further shortening of muscle occurs. Strictly speaking, the muscle is performing mechanical work while the elastic components are stretched. This can be termed internal work. Nevertheless, external mechanical work done remains zero throughout. In activities such as running and cycling, where movement does occur, we should differentiate between the mechanical work done to move the limbs and that required to move the whole body or external object.

The assessment of internal mechanical work is far from easy (Winter, 2004) because it requires assessment of the distance through which the associated muscle(s) shorten and, similarly, the distance through which series and parallel components increase as well as the determination of associated tissue-stiffness forces. We shall return to consider internal and external mechanical work below in sub-section 4.7 on efficiency.

As Table I illustrates, the terms “work” and “exercise” cannot be used synonymously yet frequently, and incorrectly, they are. Indeed, as exemplified by isometric muscle activity, it is possible to incur a metabolic demand and thus be considered to be exercising but no internal or external mechanical is done.

4.3 Power

Like work, power is a mechanical construct from classical mechanics and is a term that is frequently misapplied to sport and exercise. The history of its use can be traced to James Watt (1736–1819), who developed the atmospheric steam engine from the original design of Thomas Newcomen (1663–1729). Watt proposed a means to assess the effectiveness of steam engines that were proliferating at the beginning of the Industrial Revolution. These engines were replacing horses to drive industrial processes and so keep pace with demand for outputs. He was reportedly the first to use the term “horsepower” so as to compare the capabilities of engines with their equine equivalents. Power is:

The unit of power is the eponymous watt (W), i.e. J · s⁻¹. It is important to acknowledge that the origins of “power” are firmly rooted in steam engines and it is still used to indicate the capability of two-stroke, four-stroke or diesel internal-combustion engines that are used in automobiles, locomotives, and ships. One horsepower derived from Watt's original work is equivalent to 745.7 W, whereas the metric horsepower is 735.5 W. The former tends to be used.

Even in the context of engines, power on its own does not necessarily provide an adequate evaluation of suitability. The torque an engine produces is an important factor. This refers to the moment applied to an engine's crankshaft and manufacturers usually attempt to achieve high torque throughout the range of revolutions per minute (rev · min⁻¹). As a result, revolutions per minute can be kept comparatively low at, for example, 3000–4,000 rev · min⁻¹, whereas Formula 1 engines rev to a regulation-restricted maximum of 19,000 rev · min⁻¹.

From its origins in classical mechanics, the construct of power is now used to assess rates at which one form of energy is converted to another (Royal Society, 1975). This includes rates of energy expenditure during exercise that are determined from analyses of expired air. The term “work rate” is used frequently to describe performance during exercise but this is colloquial and should be avoided (Rogers & Cavanagh, 1984, 2008). Besides, as the definition clearly indicates, work rate must be power output. The term work rate is not recognized by the SI.

Athletes in explosive events such as horizontal and vertical jumping, sprinting, throwing, and bobsleigh are often said to be “powerful”. Indeed, commentators and authors frequently use this emotive term, but we will see in sub-section 4.6 on impulse that in most cases they are incorrect (Adamson & Whitney, 1971; Smith, 1972).

4.4 Energy

Ultimately, we are heliodependent; our energy derives from the sun. However, energy is expressed in various forms, including heat, light, electricity, chemical reactions, sound, and movement. The last of these is also termed kinetic energy. Forms of energy are converted from one to another. For instance, the food that we eat is digested and, in so doing, complex insoluble material is converted into simple soluble substances. These substances can then be transported around the body and taken up by cells. When enzymes act on these substances, the substances are termed substrates and the interaction of substrates and enzymes releases energy. The currency of energy in our cells is adenosine triphosphate (ATP).

During exercise, ATP provides the chemical energy for muscle to exert force or, if movement occurs, to convert chemical energy to kinetic energy. This change in energy indicates that work must have been performed to effect changes in the energy either within or between bodies. In conversions of chemical to mechanical energy, heat is also released and heat production – thermogenesis – is an accompaniment to exercise.

When energy release is aerobic, substrate reacts with oxygen. In anaerobic reactions, the energy is released without the use of oxygen even though there might be abundant supplies of oxygen available (Connett, Gayeski, & Honig, 1986). It is likely that the fundamental challenge in exercise is to ensure that energy requirements are met by energy availability. That is not, of course, to deny the importance of other important factors such as mental skills and technique.

Conventionally, energy is said to provide the capacity to do mechanical work but, in the context of exercise, this definition can create confusion because as we identified earlier, the conversion of metabolic energy need not necessarily lead to the expression of external work but might result instead to some other energy exchange such as heat. Mechanical work and hence movement is not always an outcome. In the context of exercise, a useful definition of energy is:

4.5 Velocity (v)

Quantities such as time (s) and distance (m) are commonly used to measure exercise performance. Similarly, mean speed (distance/time, m · s⁻¹) can be used to assess both the capability to perform exercise and the intensity of exercise. These are scalar quantities in that they indicate magnitude only. When quantities indicate magnitude and direction, they are said to be vector quantities.

Authors sometimes claim that mean running velocity or swimming velocity was some measure of metres per second. This is often neither scientific nor relevant. Consider, for instance, a 400-m runner in the inside lane of a 400-m track. The runner finishes at the same point as that from which he or she started, so their mean velocity is 0 m · s⁻¹. So, too, is the mean velocity for a 10,000-m runner on the same track. The same applies to the 100 m, 200 m, and other distances that are even-multiples of 50 m for swimmers who compete in 50-m pools.

In all of these cases, it is not mean velocity that is meaningful; speed is actually the informative and correct term. At any moment in time, instantaneous velocity defines the rate and direction of movement, but to quantify an overall effect, a composite measure (i.e. speed) is required. It might be that velocity sounds much grander but the grandness leads the unwary to grandiloquence.

4.6 Impulse

Impulse is another mechanical term from classical mechanics and emanates from Newton's second law. In Newton's Principia, this law is stated as:

Impulse is fundamental to exercise, especially when projectiles are involved. These projectiles could be implements such as shot, javelin, and discus or the body in horizontal and vertical jumping. In spite of its fundamental nature, impulse is frequently either completely overlooked or eclipsed by “power” (Adamson & Whitney, 1971; Smith, 1972). For linear motion – although the principle applies to angular motion as well – Newton's second law states that the change in momentum of a body – either as an increase or decrease – depends on the size and direction of the force applied and the duration for which the force acts. This can be expressed as:

where F is the applied force and a is the resulting acceleration. This proportion expression can be changed into an equation by introducing a constant, m:

where m is the mass of an object.

Acceleration is the rate of change of velocity, so the equation can be expressed as:

where v is final velocity, u is initial velocity, and t is the time over which the change in velocity occurs.

Consider an activity such as vertical jumping in which initial velocity is 0. The expression now becomes:

This can be rearranged to:

where F · t is the impulse of the force and m · v is the resulting momentum of the body. This is why the expression is often referred to as the impulse–momentum relationship. In most exercise settings, it is reasonable to assume that there will be no meaningful change in mass, so as impulse increases it is velocity that changes. Not only is this relationship fundamental in activities such as jumping (both horizontally and vertically), throwing, and sprinting, it is also important in multiple-sprint-type sports where “cutting” and similar changes in direction are important.

In jumping and throwing in particular, the principal factor that determines performance is velocity at take-off and release respectively. Here velocity is appropriate because it implies direction and hence angle at release or take-off and height. At this point, velocity is determined as:

Accordingly, it is the preceding impulse – the force–time integral – that determines performance. The performer has to maximize impulse through appropriate technique to manipulate the force he or she applies and the duration for which the application occurs. In events such as the shot putt, javelin, and discus, techniques are designed to allow the athlete to apply force for as long as possible. Precisely the same applies to jumping and the push-phase in bobsleigh. In many circumstances, it is optimization of the product of force and time that is critical for success and which determines the limits of performance.

Moreover, this force – that is, of course, a mean value throughout the activity – should also be as high as possible so that the resulting product of force and duration is maximized. A key and largely unanswered question is, which is the more important, magnitude of forces or duration of application? Short durations could give insufficient time for muscles to become fully activated and so lead to injury, whereas long durations could be disadvantageous because stretch–shortening cycles might not be fully harnessed.

In multiple-sprint activities such as rugby, hockey, association football, tennis, squash, badminton, netball, and basketball, sidestepping and cutting – during which accelerations and decelerations occur – are important. These accelerations and decelerations require impulse.

Force–time profiles, or force histories as they are sometimes called, can be secured from force platforms, accelerometers or kinematic analyses. The first two of these tend to be the preferred approaches because of errors inherent in the double-differentiation of displacement-time data that is required to derive acceleration using kinematics.

We can return now to sub-section 4.3 on power. The Sargent or similar type of vertical jump is often reported as a measure of “lower body power”. In impulsive activities such as jumping, power is at best a distraction and at worst irrelevant; its use in this context is simply incorrect. The unit of performance is metres and not the required watts and it is the impulse-generating capability of muscle that is the key determining factor, not its power-generating capability. Maybe to be impulsive one needs to be powerful, but it is impulse that is decisive. It is probable that the physiological mechanism for which the term power is often incorrectly used as a proxy is the rate of force development. The more rapidly a muscle can reach the desired force, the greater will be the impulse for the same given activation time.

The psychologist is probably interested in how mental skills can harness impulse-generating mechanisms, the physiologist probably wants to identify these mechanisms, and the biomechanist probably wants to identify the technique that is most effective. Clearly, all are interested but their interests are from different perspectives.

It is possible from force–time profiles mathematically to integrate the curve and so develop a velocity–time curve. This can be superimposed on the force history and when force and velocity are multiplied, the units of power (W) emerge. While at first sight this appears plausible and is dimensionally correct, the approach is misapplied because of the context. No account is taken of values that preceded or followed the calculated maximum.

It should also be noted that power, as derived from force–time data or other similar methods, represents the rate at which external mechanical work of the whole body is performed. Since in virtually all instances movement is a consequence of the action of many co-active and co-ordinated muscular actions, the calculation of a single net figure to represent this has little if any relevance to the rate at which metabolic or mechanical work is done by an individual part of the system, or to the sum of the parts to indicate whole-body work. For example, consider someone who stands and mimics the arm actions of sprinting.’ Symmetrical movement of these limbs means that the position of the body's centre of mass does not change (Winter, 1979). Similarly, while this centre of mass does move during stair climbing, for example, its path does not provide the information required to calculate both internal and external mechanical work done. These examples illustrate why it can be misleading to assess work done and hence power output based solely on the position and path of the body's centre of mass.

4.7 Efficiency

According to Winter (2004, p. 122),

What is the justification for this condemnatory statement? As before with power, the origin of the term stems from Watt's work on engines and classical mechanics. It is assessed as:

Then, as now, engineers were concerned with how well engines were using fuel to assess the cost-effectiveness of outputs. According to the SI, both the numerator and denominator in this expression are measured in joules. Normally, efficiency is expressed as a percentage, so the outcome of the product above is multiplied by 100.

As Winter (2004) examined at length, identification both of the numerator and denominator is especially challenging because each contains several considerations that are frequently overlooked. What is the problem?

First, the denominator. When exercise is supported wholly by aerobic metabolism (i.e. it is performed sub-maximally at steady state), this can probably be estimated, but estimation is not straightforward. Oxygen uptake can be determined and then multiplied by an energy-equivalent that is based on the respiratory exchange ratio (McArdle et al., 2007). This equivalent varies and usually assumes no contribution from protein, but if precise values were required, the contribution from protein would have to be identified. If non-protein equivalents will suffice, substrates are, in the extreme, exclusively fat or carbohydrate but, more likely, fuel for exercise is a mixture of the two.

Non-steady state exercise (i.e. for which there are contributions from anaerobic metabolism) markedly complicates matters. Such contributions could be either self-evident during what is clearly non-steady-state exercise or subtle as in exercise that results in the slow-component of oxygen uptake that is superimposed on the anticipated steady-state profile (Jones & Poole, 2005). Attempts to measure oxygen uptake after exercise until baseline resting values return and then use this supposedly to estimate the contribution from anaerobic metabolism are fraught with difficulties (Bangsbo, 1996; Medbø, 1996). Consideration has to be given to energy expended at rest and to move the limbs such as the legs in unloaded cycle ergometry. One or the other, both or neither of these could be subtracted from the “gross” energy expenditure to obtain a “net” value or, for that matter, a “work” or “delta” (change) response as the intensity of exercise changes (Cavanagh & Kram, 1985a, 1985b).

As if identification of the denominator wasn't challenging enough, identification of the numerator is even more difficult. In friction-braked or electrically braked cycle ergometry, providing pedalling rate is held constant, a calculation of external mechanical work done is possible. For friction-braked ergometers, if pedal rate and gearing from the pedal-crank sprocket to the flywheel are known, the distance travelled by an imaginary point on the flywheel for one pedal revolution can be determined.

Multiplication of this distance by the applied force on the ergometer and revolutions pedalled in the time that corresponded to the collection of expired air for the determination of oxygen uptake, produces mechanical work done during the period of interest. In cardiac and pulmonary physiology, this is typically one minute. Care has to be taken to recognize that this time interval does not adhere to the SI unit of time (i.e. seconds), although common usage makes the minute allowable.

However, this gives only the external mechanical work done and does not account either for frictional and other losses in the system or variations in the applied force that arise from oscillations of the resistance. According to the manufacturers, Monark ergometers have a loss of approximately 9% from input at the pedals to output at the flywheel. This loss is attributable largely to friction in bearings and between the chain and sprockets. Devices are available to calibrate friction-braked ergometers by comparing input at the pedal crank with indicated output at the flywheel, and force transducers can be mounted in series with the load and friction belts to record resistive forces. As with all instruments, this type of calibration ensures both precision and accuracy of recordings.

Another amount that tends to be overlooked is internal mechanical-work-done to move the legs and arms. This concept was introduced in sub-section 4.2 and becomes especially important if external power output is held constant by reciprocal variation of pedalling rate and resistive load; this is usually the case in attempts supposedly to investigate the effects of different cycle rates on efficiency, such as during wheelchair propulsion. Internal mechanical work done can be identified through kinematic analysis of the limbs. In essence, this involves summation for limbs of changes in potential and kinetic translational and rotational energies for each of the limb segments (Winter, 2004). It is an involved procedure but any attempt to assess the effects on efficiency of changes in cycling rate will be fundamentally flawed if internal-mechanical-work-done is not identified.

A seemingly simple task such as cycling presents several challenges. The assessment of other locomotor tasks such as running presents even more, although the principles are exactly the same (Winter, 2004). For constant-speed locomotion on a level surface or on a treadmill, there is a strong case to be made for the external work to be zero and thus the efficiency is incalculable. Only air resistance and internal friction such as in skeletal joints provide opposing horizontal forces.

It is perhaps now clearer why the term “efficiency” is misused and the implications of its use are underestimated.

4.8 Economy

Unlike efficiency, economy is a flexible term because its use is not as demanding. It tends to be used to describe oxygen uptake or heart rate responses to exercise; these are proxies for energy expenditure. As a result, the evaluation of training, for instance, could include assessments of economy. For example, in endurance-running events, training-induced reductions in oxygen uptake or heart rate at set speeds suggest that economy has improved. If maximal physiological responses had increased, the relative improvement in economy might have been even better. The most common expression of economy in running is oxygen uptake reported as ml · kg⁻¹ · km⁻¹ (Jones, 2008). This standardizes the expression of energy cost per unit distance and thus allows different speeds or modes of locomotion to be compared.

4.9 Effectiveness

Effectiveness is a term that can be independent both of efficiency and economy. For a 100-m sprinter, for instance, neither efficiency nor economy is a principal concern; the athlete simply wants to run down the track as quickly as possible. After all, the event lasts only 10 s or so. Where economy of effort does become important, perhaps even efficiency if correctly assessed, is in endurance events. Here, energy cannot be wasted because exercise might have to be sustained for hours. As a result, athletes have at least to be economical to be effective. Care has to be taken to ensure appropriate use of the terms effectiveness, efficiency, and economy.

In cycling and wheelchair propulsion, the term effectiveness has been used to describe the proportion of total applied force that acts to create the torque that drives the pedal or wheel. The ratio of the so-called “effective” force to total force has been cited as a proxy value for efficiency (Dallmeijer, van der Woude, Veeger, & Hollander, 1998). However, care is needed to determine components of the force that are actually useful. For instance, in the case of wheelchair propulsion, it is reasonable to assume that some mediolaterally oriented forces are necessary to develop the necessary contact friction to allow the transfer of the propulsive tangential force to the wheel. However, these forces are not conventionally included in the calculation of effectiveness.

4.10 Cycle ergometry

Cycle ergometry can be a source of several pitfalls, so warrants particular attention. Some of these pitfalls were identified in sub-sections 4.1 (force) and 4.3 (power). Power can be a useful measure of exercise capability and the internal-combustion or other type-of-engine analogue is useful and appropriate. For instance, a prerequisite for successful performance in track and road cycling is the ability to sustain high power output. In sprint finishes, even higher power outputs are decisive.

Cycle ergometry can also provide a useful indication of muscle function even though cycling might not be the athlete's principal mode of exercise. This introduces another consideration: force–velocity relationships outlined by Hill (1938) that are as relevant today as they were then. Basically, there is an optimum speed of shortening of muscle that maximizes power output. In turn, speed of shortening depends on the force being generated and hence the load that is moved. However, power as a measure of performance ceases to have any physiological meaning when the model is extended beyond the most simple single-muscle model.

In Wingate-type tests, for instance, the commonly applied force of 7.5% of body weight might not be great enough to achieve optimized peak power output for all of the muscles involved in the activity. This is not necessarily a problem because there are several alternative techniques that do optimize values (Winter & MacLaren, 2009). However, the ways in which applied forces are expressed are often incorrect. For example, 7.5 g · kg⁻¹ body mass is wrong. Grams and kilograms are units of mass not force and hence applied force. The expression 0.075 N · kg⁻¹ body mass is still wrong because it confuses the unit for force with the unit for mass and besides, it doesn't strictly represent 7.5% of body weight. The expression could be 0.075 N · N⁻¹ body weight but because the unit is common to both, even that can be improved to: in ratio 0.075:1 with body weight. The simplest of all is where we started: 7.5% of body weight.

It is also common to see an expression something like, “to overcome the inertia of the system, participants were given a rolling start”. This means that participants could then achieve the impossible and accelerate the system without the application of any more force. While it is indeed difficult to set the system in motion, this is attributable to the work that has to be done to overcome frictional and other factors to increase the angular momentum of the flywheel. The inertia of the system remains.

4.11 Workload

Finally, consideration is given to this term, a term that blights sport and exercise science. It has been the feature of an editorial in this Journal (Winter, 2006). In brief, it is nonsensical. It could mean the load of work that was performed, in which case the accompanying unit should be joules. It could be the opposing force in the work, in which case the unit would be newtons. It cannot be power output (W), as it is frequently claimed, nor can it be running speed (m · s⁻¹) with which it is frequently although erroneously associated. In short, as Winter (2006) stated, the term should be banished from the lexicon of exercise sciences.

5.1 Measures

Let us now consider the expressions “exercise performance” and “exercise capacity”.